Open Access

The High-Resolution Rate-Distortion Function under the Structural Similarity Index

  • Jan Østergaard1Email author,
  • Milan S. Derpich2 and
  • Sumohana S. Channappayya3
EURASIP Journal on Advances in Signal Processing20102011:857959

https://doi.org/10.1155/2011/857959

Received: 15 July 2010

Accepted: 1 November 2010

Published: 2 November 2010

Abstract

We show that the structural similarity (SSIM) index, which is used in image processing to assess the similarity between an image representation and an original reference image, can be formulated as a locally quadratic distortion measure. We, furthermore, show that recent results of Linder and Zamir on the rate-distortion function (RDF) under locally quadratic distortion measures are applicable to this SSIM distortion measure. We finally derive the high-resolution SSIM-RDF and provide a simple method to numerically compute an approximation of the SSIM-RDF of real images.

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Authors’ Affiliations

(1)
Department of Electronic Systems, Aalborg University
(2)
Department of Electronic Engineering, Federico Santa María Technical University
(3)
PacketVideo Corporation

Copyright

© Jan Østergaard et al. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.